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## Homework Statement

By vector methods, find the point on the curve x = t, y = t^2, z = 2 at which the temperature p(x,y,z) = x^2 - 6x + y^2 takes its minimum value

## Homework Equations

## The Attempt at a Solution

As far as I got was finding grad(p). From there I'm not sure where to go -- If I take the magnitude of grad(p) i can find the maximum at any point in space, but how to find the minimum I have no clue. I'm also just having trouble visualizing what exactly is being asked and how a curve and the surface relate to a physical quantity like the temperature. If anyone could help me out that would be much appreciated. Thanks a lot